Extrema Prediction and Fatigue Assessment of Highly Non-Gaussian Random Processes Using a Homogenous Reproduction Method
Publication: Journal of Engineering Mechanics
Volume 146, Issue 4
Abstract
Given a limited number of time histories of a non-Gaussian random process, it is of interest to reproduce a much greater number of samples while retaining homogenous statistical characteristics. In structural engineering, this matters to extrema prediction and fatigue assessment. Particularly when the given data exhibit strong non-Gaussianity, the issue of how to capture such stochastic characteristics while retaining the original spectral profile of the underlying process needs to be resolved. This study is an extension of the translation method that employs Hermite models to establish the relationship between the non-Gaussian process and underlying Gaussian process. Thus, unlike many other works, no information regarding a probability density function (PDF) is mandated for the translation in the present study; only central and linear moments are required. Specifically, for highly non-Gaussian processes, quartic and quintic Hermite models are discussed because the commonly used cubic Hermite model cannot yield an accurate approximation. For spectral restoration, the explicit relationship between the autocorrelation of the transformed process and that of the underlying Gaussian process is presented to retain homogeneity in the non-Gaussian characteristics. This explicit relationship also allows for more straightforward implementation of the proposed method in the time domain than the conventional PDF-based translation method. Furthermore, to remove negative power spectral contents incurred by incompatible and numerical errors, a correction procedure inspired by the iteration algorithm is used. Through comprehensive analyses of three offshore engineering problems (Morison drag force, total wave load on a jack-up platform, and stress response of a typical offshore wind turbine), the robustness and accuracy of the proposed homogeneous reproduction method in capturing both extrema and fatigue damage are affirmed.
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Data Availability Statement
All data used during this study are available from the corresponding author by request, including FEA samples and the MATLAB reproduced non-Gaussian samples in the case studies.
Acknowledgments
This research work is an expansion of the authors’ presentation at the ASCE Engineering Mechanics Conference Institute 2018 at the Massachusetts Institute of Technology, Cambridge, Massachusetts. The financial support of the China National Key Research Scheme 2016YFC0303706 is greatly appreciated.
References
Benasciutti, D., and R. Tovo. 2006. “Comparison of spectral methods for fatigue analysis of broad-band Gaussian random processes.” Probab. Eng. Mech. 21 (4): 287–299. https://doi.org/10.1016/j.probengmech.2005.10.003.
Birpoutsoukis, G., P. Z. Csurcsia, and J. Schoukens. 2018. “Efficient multidimensional regularization for Volterra series estimation.” Mech. Syst. Sig. Process. 104 (May): 896–914. https://doi.org/10.1016/j.ymssp.2017.10.007.
Bocchini, P., and G. Deodatis. 2008. “Critical review and latest developments of a class of simulation algorithms for strongly non-Gaussian random fields.” Probab. Eng. Mech. 23 (4): 393–407. https://doi.org/10.1016/j.probengmech.2007.09.001.
Borgman, L. E. 1967. Ocean wave simulation for engineering design. Berkeley, CA: California Univ., Berkeley Hydraulic Engineering Lab.
Braccesi, C., F. Cianetti, G. Lori, and D. Pioli. 2014. “Evaluation of mechanical component fatigue behavior under random loads: Indirect frequency domain method.” Int. J. Fatigue 61 (Apr): 141–150. https://doi.org/10.1016/j.ijfatigue.2013.11.017.
Capponi, L., M. Česnik, J. Slavič, F. Cianetti, and M. Boltežar. 2017. “Non-stationarity index in vibration fatigue: Theoretical and experimental research.” Int. J. Fatigue 104 (Nov): 221–230. https://doi.org/10.1016/j.ijfatigue.2017.07.020.
Chang, A., H. Li, S. Wang, and J. Du. 2017. “Probabilistic analysis and fatigue damage assessment of offshore mooring system due to non-Gaussian bimodal tension processes.” J. Ocean Univ. China 16 (4): 585–601. https://doi.org/10.1007/s11802-017-3365-x.
Conner, D. A., and J. L. Hammond. 1979. “Modelling of stochastic system inputs having prescribed distribution and covariance functions.” Appl. Math. Modell. 3 (1): 67–69. https://doi.org/10.1016/0307-904X(79)90071-4.
Deodatis, G., and R. C. Micaletti. 2001. “Simulation of highly skewed non-Gaussian stochastic processes.” J. Eng. Mech. 127 (12): 1284–1295. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:12(1284).
Ding, J., and X. Chen. 2014. “Assessment of methods for extreme value analysis of non-Gaussian wind effects with short-term time history samples.” Eng. Struct. 80 (Dec): 75–88. https://doi.org/10.1016/j.engstruct.2014.08.041.
DNV (Det Norske Veritas). 2010. Environmental conditions and environmental loads. Oslo, Norway: DNV.
Du, J., H. Li, M. Zhang, and S. Wang. 2015. “A novel hybrid frequency-time domain method for the fatigue damage assessment of offshore structures.” Ocean Eng. 98 (Apr): 57–65. https://doi.org/10.1016/j.oceaneng.2015.02.004.
Gao, S., and X. Y. Zheng. 2019. “An improved spectral discretization method for fatigue damage assessment of bimodal Gaussian processes.” Int. J. Fatigue 119 (Feb): 268–280. https://doi.org/10.1016/j.ijfatigue.2018.09.027.
Gao, S., X. Y. Zheng, and Y. Huang. 2018. “Hybrid C- and L-Moment–based Hermite transformation models for non-Gaussian processes.” J. Eng. Mech. 144 (2): 04017179. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001408.
Gioffre, M., V. Gusella, and M. Grigoriu. 2000. “Simulation of non-Gaussian field applied to wind pressure fluctuations.” Probab. Eng. Mech. 15 (4): 339–345. https://doi.org/10.1016/S0266-8920(99)00035-1.
Grigoriu, M. 1984. “Crossings of non-Gaussian translation processes.” J. Eng. Mech. 110 (4): 610–620. https://doi.org/10.1061/(ASCE)0733-9399(1984)110:4(610).
Grigoriu, M. 1998. “Simulation of stationary non-Gaussian translation processes.” J. Eng. Mech. 124 (2): 121–126. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:2(121).
Gurley, K. R., and A. Kareem. 1998. “A conditional simulation of non-normal velocity/pressure fields.” J. Wind Eng. Ind. Aerodyn. 77 (Sep): 39–51. https://doi.org/10.1016/S0167-6105(98)00130-5.
Gurley, K. R., M. A. Tognarelli, and A. Kareem. 1997. “Analysis and simulation tools for wind engineering.” Probab. Eng. Mech. 12 (1): 9–31. https://doi.org/10.1016/S0266-8920(96)00010-0.
Han, C., Y. Ma, X. Qu, M. Yang, and P. Qin. 2016. “A practical method for combination of fatigue damage subjected to low-frequency and high-frequency Gaussian random processes.” Appl. Ocean Res. 60 (Oct): 47–60. https://doi.org/10.1016/j.apor.2016.08.007.
Hosking, J. R. M. 1990. “L-moments: Analysis and estimation of distributions using linear combinations of order statistics.” J. R. Stat. Soc. 52 (1): 105–124. https://doi.org/10.1111/j.2517-6161.1990.tb01775.x.
Huang, G., Y. Luo, K. R. Gurley, and J. Ding. 2016. “Revisiting moment-based characterization for wind pressures.” J. Wind Eng. Ind. Aerodyn. 151 (Apr): 158–168. https://doi.org/10.1016/j.jweia.2016.02.006.
Jiao, G. 1996. “Probabilistic prediction of extreme stress and fatigue damage for ships in slamming conditions.” Mar. Struct. 9 (8): 759–785. https://doi.org/10.1016/0951-8339(95)00027-5.
Jiao, G., and T. Moan. 1990. “Probabilistic analysis of fatigue due to Gaussian load processes.” Probab. Eng. Mech. 5 (2): 76–83. https://doi.org/10.1016/0266-8920(90)90010-H.
Johnson, G. E. 1994. “Constructions of particular random processes.” Proc. IEEE 82 (2): 270–285. https://doi.org/10.1109/5.265353.
Jonkman, J. M., and W. D. Musial. 2010. Offshore code comparison collaboration (OC3) for IEA task 23 offshore wind technology and deployment. Golden, CO: National Renewable Energy Laboratory.
Liaw, C. Y., and X. Y. Zheng. 2001. “Inundation effect of wave forces on jack-up platforms.” Int. J. Offshore Polar Eng. 11 (2): 87–92.
Low, Y. M. 2010. “A method for accurate estimation of the fatigue damage induced by bimodal processes.” Probab. Eng. Mech. 25 (1): 75–85. https://doi.org/10.1016/j.probengmech.2009.08.001.
Lutes, L. D., and C. E. Larsen. 1990. “An improved spectral method for variable amplitude fatigue prediction.” J. Struct. Eng. 116 (4): 1149–1164. https://doi.org/10.1061/(ASCE)0733-9445(1990)116:4(1149).
Luxcey, N., H. Ormberg, and E. Passano. 2011. “Global analysis of a floating wind turbine using an aero-hydro-elastic numerical model: Part 2—benchmark study.” In Proc., ASME 2011 30th Int. Conf. on Ocean, Offshore and Arctic Engineering, 819–827. New York: American Society of Mechanical Engineers. https://doi.org/10.1115/OMAE2011-50088.
Masters, F., and K. R. Gurley. 2003. “Non-Gaussian simulation: Cumulative distribution function map-based spectral correction.” J. Eng. Mech. 129 (12): 1418–1428. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:12(1418).
Miner, M. A. 1945. “Cumulative damage in fatigue.” J. Appl. Mech. 12 (3): 159–164.
Moan, T., and X. Y. Zheng. 2009. “Quasi-static response of fixed offshore platforms to Morison-type wave loadings.” J. Offshore Mech. Arct. Eng. 135 (10): 1057–1068. https://doi.org/10.1061/(ASCE)0733-9399(2009)135:10(1057).
Moan, T., X. Y. Zheng, and S. T. Quek. 2007. “Frequency-domain analysis of non-linear wave effects on offshore platform responses.” Int. J. Non Linear Mech. 42 (3): 555–565. https://doi.org/10.1016/j.ijnonlinmec.2006.08.006.
Newland, D. E. 2005. An introduction to random vibrations, spectral and wavelet analysis. 3rd ed. New York: Dover.
Palmieri, M., M. Česnik, J. Slavič, F. Cianetti, and M. Boltežar. 2017. “Non-Gaussianity and non-stationarity in vibration fatigue.” Int. J. Fatigue 97 (Apr): 9–19. https://doi.org/10.1016/j.ijfatigue.2016.12.017.
Popescu, R., G. Deodatis, and J. H. Prevost. 1998. “Simulation of homogeneous non-Gaussian stochastic vector fields.” Probab. Eng. Mech. 13 (1): 1–13. https://doi.org/10.1016/S0266-8920(97)00001-5.
Shields, M. D., G. Deodatis, and P. Bocchini. 2011. “A simple and efficient methodology to approximate a general non-Gaussian stationary stochastic process by a translation process.” Probab. Eng. Mech. 26 (4): 511–519. https://doi.org/10.1016/j.probengmech.2011.04.003.
Shinozuka, M., and G. Deodatis. 1991. “Simulation of stochastic processes by spectral representation.” Appl. Mech. Rev. 44 (4): 191. https://doi.org/10.1115/1.3119501.
Shinozuka, M., and C. Jan. 1972. “Digital simulation of random processes and its applications.” J. Sound Vib. 25 (1): 111–128. https://doi.org/10.1016/0022-460X(72)90600-1.
SNAME (Society of Naval Architects and Marine Engineers). 2008. Recommended practice for site specific assessment of mobile jack-up units.. Jersey City, NJ: SNAME.
Spidsoe, N., and D. Karunakaran. 1997. “Effects of non-Gaussian waves to the dynamic response of jack-up platforms.” Mar. Struct. 10 (2–4): 131–157. https://doi.org/10.1016/S0951-8339(96)00021-4.
Winterstein, S. R. 1988. “Nonlinear vibration models for extremes and fatigue.” J. Eng. Mech. 114 (10): 1772–1790. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:10(1772).
Winterstein, S. R., and C. A. Mackenzie. 2013. “Extremes of nonlinear vibration: Comparing models based on moments, L-moments, and maximum entropy.” J. Offshore Mech. Arct. Eng. 135 (2): 021602. https://doi.org/10.1115/1.4007050.
Winterstein, S. R., and R. Torhaug. 1996. “Extreme jack-up response: Simulation and nonlinear analysis methods.” J. Offshore Mech. Arct. Eng. 118 (2): 103–108. https://doi.org/10.1115/1.2828817.
Yamazaki, F., and M. Shinozuka. 1988. “Digital generation of non-Gaussian stochastic fields.” J. Eng. Mech. 114 (7): 1183–1197. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:7(1183).
Yang, J. N. 1972. “Simulation of random envelope processes.” J. Sound Vib. 21 (1): 73–85. https://doi.org/10.1016/0022-460X(72)90207-6.
Yang, J. N. 1973. “On the normality and accuracy of simulated random processes.” J. Sound Vib. 26 (3): 417–428. https://doi.org/10.1016/S0022-460X(73)80196-8.
Zhao, W., and M. J. Baker. 1990. “A new stress-range distribution model for fatigue analysis under wave loading.” In Proc., Int. Conf.: Environmental Forces on Offshore Structures and their Predictions. London: Society of Underwater Technology.
Zheng, X. Y. 2003. “Nonlinear frequency-domain analysis of fixed structures subjected to Morison-type wave forces”. Ph.D. thesis, Dept. of Civil Engineering, National Univ. of Singapore.
Zheng, X. Y., and C. Y. Liaw. 2004. “Response spectrum estimation for fixed offshore structures with inundation effect included: A price’s theorem approach.” J. Offshore Mech. Arct. Eng. 126 (4): 337–345. https://doi.org/10.1115/1.1834623.
Zheng, X. Y., T. Moan, and S. T. Quek. 2007. “Non-Gaussian random wave simulation by two-dimensional Fourier transform and linear oscillator response to Morison force.” J. Offshore Mech. Arct. Eng. 129 (4): 327–334. https://doi.org/10.1115/1.2783888.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 4 • April 2020
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©2020 American Society of Civil Engineers.
History
Received: Apr 30, 2019
Accepted: Oct 2, 2019
Published online: Feb 12, 2020
Published in print: Apr 1, 2020
Discussion open until: Jul 12, 2020
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